CHAPTER IV.A FEW WORDS ABOUT THE MÈTRE.[edit]
The idea of an invariable and constant system of measurement,
of which nature herself should furnish the exact
value, may be said to have existed in the mind of man from
the earliest ages. It was of the highest importance, however,
that this measurement should be accurately determined,
whatever had been the cataclysms of which our
earth had been the scene, and it is certain that the ancients
felt the same, though they failed in methods and appliances
for carrying out the work with sufficient accuracy.
The
best way of obtaining a constant measurement was to connect
it with the terrestrial sphere, whose circumference must
be considered as invariable, and then to measure the whole
or part of that circumference mathematically.
The ancients
had tried to do this, and Aristotle, according to some
contemporary philosophers, reckoned that the stadium, or
Egyptian cubit, formed the hundred-thousandth part of the
distance between the pole and the equator, and Eratosthenes
in the time of the Ptolemies, calculated the value
of a degree along the Nile, between Syene and Alexandria,
pretty correctly; but Posidonius and Ptolemy
were not sufficiently accurate in the same kind of geodetic
operations that they undertook; neither were their
successors.
Picard, for the first time in France, began to regulate the
methods that were used for measuring a degree, and in
1669, by measuring the celestial and terrestrial arcs between
Paris and Amiens, found that a degree was equal to
57,060 toises, equivalent to 364,876 English feet, or about
69.1 miles.
Picard's measurement was continued either
way across the French territory as far as Dunkirk and
Collioure by Dominic Cassini and Lahire (1683—1718),
and it was verified in 1739, from Dunkirk to Perpignan,
by Francis Cassini and Lacaille; and at length Méchain
carried it as far as Barcelona in Spain; but after his death
(for he succumbed to the fatigue attending his operations)
the measurement of the meridian in France was interrupted
until it was subsequently taken up by Arago and Biot in
1807. These two men prolonged it as far as the Balearic Isles,
so that the arc now extended from Dunkirk to Formentera,
being equally divided by the parallel of lat. 45° N., half
way between the pole and the equator; and under these
conditions it was not necessary to take the depression of
the earth into account in order to find the value of the
quadrant of the meridian. This measurement gave 57,025
toises as the mean value of an arc of a degree in France.
It can be seen that up to that time Frenchmen especially
had undertaken to determine that delicate point, and it was
likewise the French Convention that, according to Talleyrand's
proposition, passed a resolution in 1790, charging
the Academy of Sciences to invent an invariable system of
weights and measures. Just at that time the statement
signed by the illustrious names of Borda, Lagrange, Laplace,
Monge, and Condorcet, proposed that the unit of
measure should be the ”mètre” the ten-millionth part of the
quadrant of the meridian; and that the unit of weight
should be the ”gramme”, a cubic centimètre of distilled water
at the freezing-point; and that the multiples and subdivisions
of every measure should be formed decimally.
Later, the determinations of the value of a terrestrial
degree were carried on in different parts of the world, for
the earth being not spherical, but elliptic, it required much
calculation to find the depression at the poles.
In 1736, Maupertuis, Clairaut, Camus, Lemonnier, Outhier,
and the Swedish Celsius measured a northern arc in
Lapland, and found the length of an arc of a degree to
be 57,419 toises.
In 1745, La Condamine, Bouguer, and
Godin, set sail for Peru, where they were joined by the
Spanish officers Juan and Antonio Ulloa, and they then
found that the Peruvian arc contained 56,737 toises.
In 1752, Lacaille reported 57,037 toises as the length of
the arc he had measured at the Cape of Good Hope.
In 1754, Father Boscowitch and Father le Maire began
a survey of the Papal States, and in the course of their
operations found the arc between Rome and Rimini to be
56,973 toises.
In 1762 and 1763, Beccaria reckoned the degree in Piedmont
at 57,468 toises, and in 1768, the astronomers Mason
and Dixon, in North America, on the confines of Maryland
and Pennsylvania, found that the value of the degree in
America was 56,888 toises.
Since the beginning of the 19th century numbers of other
arcs have been measured, in Bengal, the East Indies, Piedmont,
Finland, Courland, East Prussia, Denmark, &c., but
the English and Russians were less active than other nations
in trying to decide this delicate point, their principal
geodetic operation being that undertaken by General Roy
in 1784, for the purpose of determining the difference of
longitude between Paris and Greenwich.
It may be concluded from all the above-mentioned measurements
that the mean value of a degree is 57,000 toises,
or 25 ancient French leagues, and by multiplying this mean
value by the 360 degrees contained in the circumference,
it is found that the earth measures 9000 leagues round.
But, as may be seen from the figures above, the measurements
of the different arcs in different parts of the world do
not quite agree. Nevertheless, by taking this average of
57,000 toises for the value of a degree, the value of the
metre, that is to say, the ten-millionth part of the
quadrant of the meridian, may be deduced, and is found
to be 0.513074 of the whole line,[1]
or 39.37079 English inches.[2]
In reality, this value is rather too small, for
later calculations (taking into account the
depression of the earth at the poles,
which is 1/299.15 and not 1/334, as was
thought at first) now give nearly 10,000,856 mètres instead
of 10,000,000 for the length of the quadrant of the meridian.
The difference of 856 mètres is hardly noticeable in such
a long distance; but nevertheless, mathematically speaking,
it cannot be said that the mètre, as it is now used,
represents the ten-millionth part of the quadrant of the
terrestrial meridian exactly; there is an error of about
1/5000 of a line,[3]
i.e. 1/5000 of the twelfth part of an inch.
The mètre, thus determined, was still not adopted by all
the civilized nations. Belgium, Spain, Piedmont, Greece,
Holland, the old Spanish colonies, the republics of the
Equator, New Granada, and Costa Rica, took a fancy to
it immediately; but notwithstanding the evident superiority
of this metrical system to every other, England
had refused to use it.
Perhaps if it had not been for the
political disturbances which arose at the close of the
18th century, the inhabitants of the United Kingdom
would have accepted the system, for when the Constituent
Assembly issued its decree on the 8th of May,
1790, the members of the Royal Society in England were
invited to co-operate with the French Academicians. They
had to decide whether the measure of the mètre should be
founded on the length of the pendulum that beats the
sexagesimal second, or whether they should take a fraction
of one of the great circles of the earth for a unit of
length; but events prevented the proposed conference, and
so it was not until the year 1854 that England, having long
seen the advantage of the metrical system, and that scientific
and commercial societies were being founded to spread
the reform, resolved to adopt it.
But still the English
Government wished to keep their resolution a secret until
the new geodetic operations that they had commenced
should enable them to assign a more correct value to the
terrestrial degree, and they thought they had better act in
concert with the Russian Government, who were also
hesitating about adopting the system.
A Commission of
three Englishmen and three Russians was therefore chosen
from among the most eminent members of the scientific
societies, and we have seen that they were Colonel Everest,
Sir John Murray, and William Emery, for England; and
Matthew Strux, Nicholas Palander, and Michael Zorn, for
Russia.
The international Commission having met in
London, decided first of all that the measure of an arc of
meridian should be taken in the Southern hemisphere, and
that another arc should subsequently be measured in the
Northern hemisphere, so that from the two operations
they might hope to deduce an exact value which should
satisfy all the conditions of the programme.
It now remained
to choose between the different English possessions
in the Southern hemisphere, Cape Colony, Australia, and
New Zealand. The two last, lying quite at the antipodes
of Europe, would involve the Commission in a long
voyage, and, besides, the Maoris and Australians, who
were often at war with their invaders, might render the
proposed operation difficult; while Cape Colony, on the
contrary, offered real advantages. In the first place, it
was under the same meridian as parts of European Russia,
so that after measuring an arc of meridian in South Africa,
they could measure a second one in the empire of the
Czar, and still keep their operations a secret; secondly,
the voyage from England to South Africa was comparatively
short; and thirdly, these English and Russian
philosophers would find an excellent opportunity there
of analyzing the labours of the French astronomer Lacaille,
who had worked in the same place, and of proving whether
he was correct in giving 57,037 toises as the measurement
of a degree of meridian at the Cape of Good Hope.
It
was therefore decided that the geodetic operation should
be commenced at the Cape, and as the two Governments
approved of the decision, large credits were opened,
and two sets of all the instruments required in a triangulation
were manufactured. The astronomer William
Emery was asked to make preparations for an exploration
in the interior of South Africa, and the frigate “Augusta,”
of the royal navy, received orders to convey the members
of the Commission and their suite to the mouth of the
Orange River.
It should here be added, that besides the scientific
question, there was also a question of national vainglory
that excited these philosophers to join in a common labour;
for, in reality, they were anxious to out-do France in her
numerical calculations, and to surpass in precision the
labours of her most illustrious astronomers, and that in
the heart of a savage and almost unknown land. Thus
the members of the Anglo-Russian Commission had resolved
to sacrifice every thing, even their lives, in order
to obtain a result that should be favourable to science,
and at the same time glorious for their country.
And
this is how it came to pass that the astronomer William
Emery found himself at the Morgheda Falls, on the banks
of the Orange River, at the end of January, 1854.
1^ `whole line' is an invention by the translator.
Verne states qui se trouve être de 0.513074;
which works out to be 0.513074 (toises).
2^ By using English units, the translator has messed up the
preciseness of Verne's work. Verne wrote trois pieds onze lignes
deux cent quatre-vingt-seize millièmes de ligne; three feet and 11.296 lines
(i.e. 443.296 lines, the line being 1/12 of a French inch).
This was the definition of the metre
adopted by the French law of 1799.
The toise is six French feet, or 864 lines,
and the metre 443.296/864=0.513074074... toises.
Note that in imperial units, the inch is defined as 0.0254 metres,
so the metre is 1/0.0254=39.37007874 inches.
3^
Verne states deux dix millièmes de ligne; about 0.00045 millimetres,
or 4 metres over the entire quadrant. This is inconsitent with the
difference of 856 metres stated previously.
The polar circumference of the Earth is currently measured at 40,007.86 km,
meaning that the error is slightly less than 2 kilometres per quadrant, or 0.2 millimetres
per metre.
